Non-thermal processes in cosmological simulations

1.6 MB·English

by  K. Dolag

SSRv manuscript No.
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Non-thermal processes in cosmological simulations
K. Dolag · A.M. Bykov · A. Diaferio
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n Received: 17September 2007;Accepted: 7November2007
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7 Abstract Non-thermal components are key ingredients for understanding clusters of
galaxies. In the hierarchical model of structure formation, shocks and large-scale tur-

] bulence are unavoidable in the cluster formation processes. Understanding the ampli-
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fication and evolution of the magnetic field in galaxy clusters is necessary for mod-
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elling both the heat transport and the dissipative processes in the hot intra-cluster
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o plasma. The acceleration, transport and interactions of non-thermal energetic parti-
r cles are essential for modelling the observed emissions. Therefore, the inclusion of the
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s non-thermal components will be mandatory for simulating accurately the global dy-
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namical processes in clusters. In this review, we summarise the results obtained with
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thesimulations of theformation of galaxy clusters which address theissues of shocks,

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magnetic field,cosmic ray particles and turbulence.
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8 Keywords cosmology: theory, large-scale structure of universe; acceleration of
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particles; hydrodynamics;magnetic fields; method: numerical, N-body simulations
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1 Introduction
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0 Withintheintra-clustermedium(ICM),thereareseveralprocesseswhichinvolvenon-
: thermalcomponents,suchasthemagneticfieldandcosmicrays(CRs).Atfirstglance,
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i many of these processes can bestudied numerically in simplified configurations where
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one can learn how the individual processes work in detail. For example, there are
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K.Dolag
Max-Planck-Institut fu¨r Astrophysik, P.O. Box 1317, D-85741 Garching, Germany E-mail:
[email protected]
A.M.Bykov
A.F. Ioffe Institute of Physics and Technology, St. Petersburg, 194021, Russia E-mail:
[email protected]ffe.ru
A.Diaferio
DipartimentodiFisicaGenerale“AmedeoAvogadro”,Universita`degliStudidiTorino,Torino,
Italy
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via P. Giuria 1, I-10125,
Torino,Italy
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investigations which consider magneto-hydro-dynamical (MHD) simulations of cloud-
wind interactions (see Gregori et al. 2000, and references therein) or simulate the
rise of relic radio bubbles (see Jones & DeYoung 2005; Reynoldset al. 2005, and
references herein).Such work usually focuses on therelevance of CRs, turbulenceand
thelocalmagneticfieldswithinandaroundthesebubbles.Inthisreview,wewillinstead
concentrate on simulations of non-thermal phenomena, which aim at understanding
therelevanceofthesephenomenaforgalaxy clusterpropertiesoratunveilingpossible
origins of the non-thermal radiation. So far, firm evidence for the presence of non-
thermalemission(atradiowavelengths)andforthepresenceofcosmologicallyrelevant
extendedmagneticfieldshasbeenfoundonlyingalaxyclusters;infilamentsonlyweak
limits have been found so far. For a more detailed discussion see the reviews on radio
observationsbyRephaeli et al.(2008)-Chapter5,thisvolume,andFerrari et al.2008
- Chapter 6, this volume.
2 Possible origins of non-thermal components within the large-scale
structure (LSS)
The origin of magnetic fields and of CRs in galaxy clusters is still under debate. The
varietyofpossiblecontributorstomagneticfieldsrangesfromprimordialfields,battery
anddynamofieldstoalltheclasses ofastrophysicalobjects whichcancontributewith
theirejecta.Thelatterpossibilityissupportedbytheobservationofmetalenrichment
of the ICM, which is due to the ejecta of stars in galaxies, see Werneret al. 2008 -
Chapter16,thisvolume,andSchindler& Diaferio2008-Chapter17,thisvolume.The
magneticfieldsproducedbyallthesecontributorswillbecompressedandamplifiedby
theprocessofstructureformation.Theexactamountofamplificationandtheresulting
filling factor of the magnetic field will depend on where and when the contributor is
thought to bemore efficient.
CRs are produced at shocks, both in supernova remnants and in cosmological ac-
cretionandmergershocks.Furthermore,activegalacticnuclei(AGN)andradiogalax-
ies contribute to the CR population. CR protons can also produce CR electrons via
hadronic reactions with thethermal plasma, leading tothe so-called secondary CRs.
2.1 Possible origins of magnetic fields
Magnetic fields can be produced either at relatively low redshift (z ∼ 2−3) or at
high redshift (z &4). In the former case, galactic winds (e.g. V¨olk & Atoyan 2000) or
AGN ejecta (e.g. Enßlin et al. 1997; Furlanetto& Loeb 2001, and references therein)
producemagneticfields‘locally’,e.g.withintheproto-clusterregion.Inthelattercase,
themagneticfieldseedscanalsobeproducedbyanearlypopulationofdwarfstarburst
galaxies or AGN before galaxy clusters form gravitationally bound systems.
One of the main arguments in favour of the ’low-redshift’ models is that the high
metallicity observedintheICMsuggests thatasignificantenrichmentoccurredinthe
past due to galactic winds or AGN. Winds and jets should carry magnetic fields to-
getherwiththeprocessedmatter.Ithasbeenshownthatwindsfromordinarygalaxies
give rise to magnetic fields which are far weaker than those observed in galaxy clus-
ters, whereas magnetic fields produced by the ejecta of starburst galaxies can be as
large as 0.1µG. Clearly, this class of models predicts that magnetic fields are mainly
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concentrated inandaround galaxies andwithin galaxy clusters. Notethatifthemag-
neticpollutionhappensearlyenough(aroundz∼3),thesefieldswillbeamplifiednot
only bytheadiabatic compression of theproto-cluster region, butalso byshear flows,
turbulent motions, and merging events during the formation of the cluster. Shocks
are expected to be produced copiously during the non-linear stage of the LSS forma-
tion (see below). Recent detailed studies of shock propagation revealed the presence
of specific instabilities driven by energetic accelerated particles (Bell & Lucek 2001;
Vladimirov et al. 2006). Such instabilities result in a strong, non-adiabatic amplifica-
tion of an upstream magnetic field seed which converts an appreciable fraction of the
shock ram pressure intomagnetic fields.
In the ’high-redshift’ models of the magnetic field generation, the strength of the
field seed is expected to be considerably smaller than in the previous scenario, but
the adiabatic compression of the gas and the shear flows driven by the accretion of
structures can give rise to a considerable amplification of the magnetic fields. Several
mechanisms have been proposed to explain the origin of magnetic field seeds at high
redshift. Someof them are similar to those discussed above, differing only in the time
whenthemagneticpollutionisassumedtotakeplace.Inthepresentclassofmodelsthe
magneticfieldseedsaresupposedtobeexpelledbyanearlypopulationofAGNordwarf
starburst galaxies at a redshift between 4 and 6 (Kronberget al. 1999); this process
wouldmagnetisealargefractionofthevolume.Recently,thevalidityofsuchascenario
hasbeenconfirmedbyasemi-analyticmodellingofgalacticwinds(Bertone et al.2006).
Alternative models invoke processes that took place in the early universe. Indeed,
the presence of magnetic fields in almost all the regions of the universe suggests that
they may have a cosmological origin. In general, most of the ‘high-z models’ predict
magnetic field seeds filling the entire volume of the universe. However, the assumed
coherence length of the field crucially depends on the details of the model. While
scenarios based on phase transitions give rise to coherence lengths which are so small
thatthecorrespondingfieldshaveprobablybeendissipated,magneticfieldsgenerated
atneutrinoorphotondecouplingarethoughttohaveamuchhigherchanceofsurviving
until the present time. Another (speculative) possibility is that the field seed was
produced during inflation. In this case, the coherence length can be as large as the
Hubbleradius. See Grasso & Rubinstein (2001) for a review.
Magneticfieldseedscanalsobeproducedbytheso-calledBiermannbatteryeffect
(Kulsrud et al. 1997; Ryu et al. 1998). The idea here is that merger/accretion shocks
related to the hierarchical structure formation process give rise to small thermionic
electriccurrentswhich,inturn,maygeneratemagneticfields.Thebatteryprocesshas
the attractive feature of being independent of unknown physics at high redshift. Its
drawbackisthat,duetothelargeconductivityoftheICM,itcangiverisetoverytiny
magneticfields,oforder10−21 Gatmost.Onethereforeneedstoinvokeasubsequent
turbulentdynamo toboost thefield strength to theobserved level.
Suchaturbulentamplification,however,cannotbesimulatednumericallyyet,mak-
ing it quite difficult to predict how it would proceed in a realistic environment. It is
clearthatoneexpectsthelevelofturbulencetobestronglydependentontheenviron-
ment, and that it should appear mostly in high-density regions like collapsed objects.
While energetic events, such as mergers of galaxy clusters, can easily be effective at
drivingtherequiredlevelsofturbulence,itishardertounderstandhowturbulentam-
plification would work in relatively quiet regions like filaments. Here, magnetic fields
can be rather amplified by the shocks which originate during the LSS formation, as
mentionedat thebeginningofthissection. Lackingatheoretical understandingofthe
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turbulentamplification,itisthereforenotstraightforwardtorelatetheveryweakfield
seedsproducedbythebatteryprocesstothemagneticfieldsobservedtoday.Attempts
toconstructsuchmodels,basedoncombiningnumericalandanalyticalcomputations,
have not yet been reported to successfully reproduce the observed scaling relations of
themagnetic fields in galaxy clusters.
2.2 Possible origins of CRs
There are many possible contributors to the CR population in the ICM. AGN and
stellar activity in cluster galaxies are believed to be a significant source of CRs in the
ICM. Furthermore, cluster accretion shocks of high Mach numbers (typically above
100)andofsizesofmegaparsecorlargerarewidelyacceptedtobepossibleCRsources
with nuclei accelerated up to ∼ 109 GeV (e.g. Norman et al. 1995). Cluster mergers
generateinternalshocks(ofmoderateMachnumbers,typicallybelow4)whichprovide
most of theICM gas heating(see e.g. Kang et al. 2005), butare also likely toconvert
a non-negligible fraction (& 10 %) of their power into CRs.
AGN outflows dissipate their kinetic energy and Poynting fluxes into the ICM
providing additional non-gravitational ICM heating and, thus, a plausible feedback
solutiontothecoolingflowproblem(e.g.Binney & Tabor1995;Churazov et al.2003).
Recent XMM-Newton observations of the cluster MS 0735+7421 (Gitti et al. 2007)
revealed that a powerful AGN outburst deposited about 6×1061 erg into the ICM
outsidethecoolingregionofradius∼100kpc.RelativisticoutflowsofAGNarelikelyto
beanessentialsourceofsuper-thermalparticlesinclusters.ApowerfulrelativisticAGN
jet could deposit up to 1062 erg into a relativistic particle pool during a duty cycle of
about∼50Myr.Apotentialsourceofenergeticparticlesaresub-relativisticionswith
energy∼100MeVthatareevaporatedfrom anAGN,whichaccretesmassintheion-
supportedtoriregime(e.g.Rees et al.1982).Acertainfractionoftheenergeticparticles
couldescapetheflowsandavoidfastcoolingduetocollectiveeffectsinthecentralparts
of the cluster. Re-acceleration of that non-thermal population by inner shocks inside
the cluster can provide a long-lived non-thermal component that contributes to the
total pressure of theICM.
Star formation activity in galaxies is another source of CRs in clusters of galaxies
(e.g. V¨olk et al. 1996, and references therein). The combined action of supernovae
and winds of early-type stars leads to the formation of a hot, X-ray emitting, slowly
expandingsuperbubblefilledwithlarge-scale (tensofparsecs) compressibleMHDmo-
tions(e.g.rarefactions) andshocks.Whenthestarbursteventisenergeticenough,the
superbubble may expand beyond the disk of the parent galaxy and produce a super-
wind that supplies the intergalactic medium with metals ejected by supernovae and
CRs. The superwinds havebeen seen with Chandra in some starburst galaxies: M 82,
Arp220andNGC253.Inthesuperwindscenario,theCRejectionistightlyconnected
withthemetalenrichmentofthecluster(Schindler& Diaferio 2008-Chapter17,this
volume).
Bykov (2001) argues that non-thermal particle acceleration can favourably occur
in correlated supernovae events and powerful stellar winds with great energy release,
which generate interacting shock waves within superbubbles. The acceleration mech-
anism provides efficient creation of a non-thermal nuclei population with a hard low-
energy spectrum; this population can transport a substantial fraction (∼ 30%) of the
kinetic energy released by thesupernovaeand bythewinds of youngmassive stars.
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Fig. 1 Thesimulatedefficiencyof conversionof shockandbulkMHDmotions rampressure
powertotheCRsatdifferentstagesofclusterevolution.Theefficiencyisdefinedasavolume
averagedfractionoftheclusterlarge-scalemotionspower transferredtoCRs.Thesimulation
wasdoneforamodelofCRaccelerationbyanensembleofshocksandMHD-turbulentmotions
describedinBykov(2001),adopted forclustersofgalaxies.TheMHDturbulenceinacluster
of a Mpc size was initiated with the Gaussian bulk velocity dispersion of 2000 kms−1 at a
scaleof100kpc.
AbrightphaseinthegalaxyevolutioncanbethesourceoftherelicCRsinclusters.
Energetic nucleican bestored in clustermagnetic fieldsfor several Hubbletimes (e.g.
Berezinsky et al. 1997). The presence of these nuclei produces a diffuse flux of high-
energy γ and neutrino radiation due to the interaction of the CRs with the ICM
(V¨olk et al. 1996; Enßlin et al. 1997). The resulting flux depends on the ICM baryon
density.
A physical model of particle acceleration by the ensemble of inner shocks in the
ICM could be similar to the superbubble model. The sub-cluster merging processes
and the supersonic motions of dark matter halos in the ICM are accompanied by
the formation of shocks, large-scale flows and broad spectra of MHD-fluctuations in
a tenuous intra-cluster plasma with frozen-in magnetic fields. Vortex electric fields
generated by the large-scale motions of highly conductive plasma harbouring shocks
resultinanon-thermaldistributionofthechargednuclei.Thefreeenergyavailablefor
the acceleration of energetic particles is in the ram pressure of the shocks and in the
large-scale motions.
The most studied way to transfer the power of theMHD motions to the energetic
particlepopulationistheFermi-typeacceleration(seee.g.thereviewbyBlandford & Eichler
1987 and Bykov et al. 2008 - Chapter7, this volume).An important ingredient of the
energetic particle acceleration byshocks andlarge-scale MHD motions isthepresence
of small-scale MHD turbulence, which is necessary to scatter relativistic particles and
tomaketheirpitch-angleisotropic. Thescale ofthefluctuationsrequiredforthereso-
nant scattering of a particle of energy ∼ 1 GeV is about 3× 1012B−−61 cm, where B−6
is the local mean magnetic field in µG. The scale is some 10–11 orders of magnitude
smallerthanthebasicenergyscaleofthesystem;thustheoriginandthemaintenance
mechanisms of such small scale turbulenceis a serious problem.
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Fig. 2 ThetemporalevolutionoftheparticledistributionfunctioninaclusterofaMpcsize
and a Gaussian bulk velocity dispersion of about 2000 kms−1 at a scale of 100 kpc. The
curves labelledas 1, 2, 3correspond to0.1, 0.3and1Gyr age of the cluster.Mono-energetic
proton injection at energy 10 keV (p0 is the injection momentum). The injection efficiency
(seeFig.1)wasassumedtobeabout10−3.Thepowerconversionefficiencyforthemodelwas
alreadyillustratedinFig.1.
In non-linear models of particle acceleration by strong MHD shocks the presence
of turbulence could be supported by the CR instabilities themselves (see e.g. recent
non-linear Monte-Carlo simulations by Vladimirov et al. 2006). Direct MHD cascade
of energy to small scale turbulence is also possible, but the small scale fluctuations
are highly anisotropic in that case (see e.g. Biskamp 2003). Moreover, the cascade
properties are still poorly known at the scales close to the Coulomb mean free path
where thetransition from the collisional to thecollisionless plasma regime occurs.
Theparticledistributionwithinasystemwithmultipleshocksandwithlarge-scale
plasmamotionsishighlyintermittent,becauseithasstrongpeaksatshocksandanon-
steadymeanCRbackground.ByusingthekineticequationsgivenbyBykov(2001),one
can construct a model of the temporal evolution of the particle distribution function,
which accounts for the non-linear effect of the reaction of the accelerated particles on
theshockturbulenceinsidethecluster.InFig.1weshowtheefficiencyofaconversion
into CRs of the power of shocks and the bulk plasma motions of a scale of about
100 kpc. One may note that, while the efficiency could be as high as 30 % for some
relatively short period of time, the efficiency is typically ∼ 10 % for most of thetime.
Fig. 2 shows the temporal behaviour of theparticle spectra on a Gyrtime scale.
Non-thermalparticlesandmagneticfieldscouldcontributetothetotalpressureof
the ICM. In the particular model described above a substantial energy density could
be stored in protons of energy below 200 MeV. Protons of that energy level produce
very little high energy emission and therefore it is rather difficult to constrain that
component directly from theobservational data which are currentlyavailable.
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3 Shocks in the LSS and clusters
As described in the previous section, shocks can play a crucial role as source of non-
thermalcomponentsingalaxyclusters.Therefore, asignificanteffortisspenttoinves-
tigate thedistribution and theevolution of shocks during structureformation.
In early simulations of the formation of cosmological structures, it was already
noticedthatshocksarethemainsourceoftheICMheating(seeQuilis et al.1998, and
references therein). In numerical simulations, two classes of shocks can beidentified.
Thefirst one is theaccretion shocks surroundingtheforming objects, namely fila-
mentsorgalaxyclusters.Inthecaseofgalaxyclusters,mostshocksarequasi-spherical
andtheirpositionwithrespecttothecentreoftheclustergrowswithtime(shocktrav-
elling outwards). These shocks can be associated with the accretion of diffuse matter
which is relatively cold. These shocks provide a first step towards the virialisation of
an initially supersonic accreting flow. The radius of the accretion shock (for a quasi-
spherical cluster at z = 0) is typically two times the virial radius. As the typical
temperature and density of the upstream gas is quite low, such shocks can have very
large Mach numbers(≫10).
The second class of shocks in galaxy clusters arises from the merging of substruc-
tures. The gas in gravitationally bound substructures is much denser than the diffuse
ICM; therefore it cannot be stopped in the accretion shock and it continues to move
with the substructure through the gas, which is mostly virialised. The substructures,
whichhavevelocitieslargerthanthesoundvelocityofthehotICM,drivetheso-called
merger shocks. These shocks are initiated within the ICM which has been already
shock-heated, and therefore they typically have modest Mach numbers (below ≈4).
The merger shocks propagate within the dense ICM and are likely to be the main
contributortotheglobalenergydissipationwithintheICM(seePfrommer et al.2006,
and references therein). As these shocks are primarily driven by gravitational attrac-
tion,non-gravitationalprocesses(likecoolingorfeedbackbystarformationprocesses)
do not significantly affect the global energy dissipation (see Kang et al. 2007). The
rampressuredissipationprocessinshockswithinthecollisionless plasmaisnon-trivial
because of the role of long-lived non-thermal components, namely magnetic fields,
MHD-wavesandenergeticparticles(seefordetailsBykov et al.2008 -Chapter7,this
volume).Thecomplexmulti-scalestructureofashockmodifiedbyenergeticCRs(e.g.
wherethebackreaction oftheCRsonthethermalplasmaisstrongenoughtochange
the thermodynamical states of the plasma in addition to the shock itself) cannot be
resolved properly in LSS simulations.
TheefficiencyofenergisingCRsbyshocksstronglydependsonanumberoffactors.
Among the most important factors, we have (i) the upstream magnetic field of the
shock,(ii) theplasmaparameterβ =M2a/M2s (ratioofthermaltomagneticpressure,
hereexpressedbytheMachnumbersMaandMswithrespecttotheAlfv´enandsound
velocity respectively), (iii) the inclination of the upstream field of the shock, and (iv)
the presence of a pre-existing CR population produced by the accretion shock or in
star-forming regions.
ThedistributionoftheMachnumbersoftheshockswithinthecosmological struc-
turecanbederivedfromsemi-analyticalmodelling(seeGabici & Blasi2003;Pavlidou & Fields
2006, and references therein), as well as directly from cosmological simulations (see
Miniati et al. 2000; Ryu et al. 2003; Pfrommer et al. 2006; Kang et al. 2007, and ref-
erences therein). An example is shown in Fig. 3. There are significant differences in
the strength and the distribution of the shocks found in different works: this fact has
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Fig. 3 Shocks detected ina cosmological simulation of acubic volume with aside length of
100 Mpc, resolved with 5123 grid points. The figure shows the kinetic energy flux per unit
comovingvolumethroughsurfacesofexternalandinternalshockswithMachnumberbetween
logM andlogM+d(logM)atdifferentredshifts(solid,z=0todotted,z=2).FromRyuetal.
(2003).
strongconsequenceson thepredicted amountand therelativeimportance ofCRsand
their energy with respect to the thermal energy of the ICM. Note that part of the
confusion, specially intheearly work,iscaused byalackof resolution within thesim-
ulations, which prevents internal shocks from being properly resolved (see Ryuet al.
2003; Pfrommer et al. 2006); further confusion originates from the influence of other,
non-thermal processes (like preheating) on the inferred Mach number of the external
shocks (see Pfrommer et al. 2006; Kang et al. 2007). Moreover, differences in the un-
derlying hydrodynamic simulations as well as in the shock detection, mostly done in
a post processing fashion, can contribute to differences in the results. Nevertheless,
there is a qualitative agreement in the case of simulated internal shocks between the
simulations done byRyuet al. (2003) and Pfrommer et al. (2006).
4 Evolution of magnetic fields in simulations
4.1 Local amplification of magnetic fields
AverybasicprocesswhichamplifiesmagneticfieldsisrelatedtotheKelvin-Helmholtz
(KH) instabilities driven by shear flows, which are common during the formation of
cosmicstructures.Birk et al.(1999)performedadetailedstudyofsuchanamplification
within the outflows of starburst galaxies, where the KH timescale should be ≈ 4×
105 years (see Fig. 4). By using a Cartesian resistive MHD code they found that
theamplificationfactorofthemagneticfieldmainlydependsontheinitialratioofthe
magnetictothekineticenergyandonlymildlydependsontheassumedresistivity.They
concluded that such a process could indeed explain why the magnetic field observed
in the halo of starburst galaxies is significantly higher than what is expected from
the magnetic fields observed within galactic disks. When applied to a cluster core
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Fig. 4 Resistive,MHDsimulationofaflow whichisKHinstableat the interface separating
the left and right halve of the simulated volume. Shown is the magnetic field (y-component)
in units of the initial magnetic field after evolving the KH instability (inlay) and the time
evolutionofthe(relative)magneticfieldamplitudefordifferentvaluesofthechosenresistivity
andinitialmagneticfield.Timeisinunits oftheAlfv´enictransittime(4000 year). Triangles
andstarsareforaninititalmagneticfieldof10µG,crossesanddiamondsforatentimeslarger
field.StarsanddiamondshaveamagneticReynoldsnumberof100,trianglesandcrosseshave
atentimeslargermagneticReynoldsnumber.FromBirketal.(1999).
environment,theKHtimescaleturnsouttobe107 years;thistimescalemakestheKH
instability an interesting process to amplify weak magnetic fields.
Itisquiteexpectedthat mergereventsandaccretion of material ontogalaxy clus-
ters will drive significant shear flows within the ICM. Extensive MHD simulations
of single merging events performed using the Eulerian code ZEUS (Stone& Norman
1992a,b) demonstrated that merger events are effective at amplifying magnetic fields
(Roettiger et al. 1999b). In particular these authors found that the field initially be-
comes quite filamentary, as a result of stretching and compression caused by shocks
and bulk flows during infall; at this stage only a minimal amplification occurs. When
the bulk flow is replaced by turbulent motions (e.g., eddies), the field amplification is
morerapid,particularlyinlocalizedregions,seeFig.5.Thetotalmagneticfieldenergy
is found to increase by nearly a factor of three with respect to a non-merging cluster.
In localised regions (associated with high vorticity), the magnetic energy can increase
by a factor of 20 or more.
Apowerspectrumanalysisofthemagneticenergyshowedthattheamplificationis
largelyconfinedtoscalescomparabletoorsmallerthantheclustercores:thisindicates
that the core dimensions define the injection scale. It is worth taking notice that the
previous results can beconsidered as a lower limit on thetotal amplification, because
ofthelackofresolution.Furthermore,itisquitelikelythatagalaxyclusterundergoes
more than one of these events during its formation process, and that the accretion of
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Fig. 5 The evolution of (the logarithm of) the gas density (left column), the gas tempera-
ture (central column), and (the logarithm of) the magnetic pressure (right column) in two-
dimensionalslicestakenthroughthecoreofaclusterinamajormergerphaseintheplaneof
the merger. Each row refers to different epochs: t=0 (i.e. the time of the core coincidence),
t = 1.3, t = 3.4, and t = 5.0 Gyr, from top to bottom. Each panel is 3.75×3.75 Mpc. The
mergingsubclusterentersfromtheright.FromRoettigeret al.(1999b).
smallerhaloesalsoinjectsturbulentmotionsintotheICM:consequently,themagnetic
fieldamplificationwithingalaxyclusterswillbeevenlarger.Adetaileddiscussionofthe
amplificationofmagneticfieldintheclusterenvironment,usingvarioussimulationsof
driventurbulence,canbefoundinSubramanian et al.(2006);theseauthorsshowthat
turbulentprocesses can providereasonable strength and length scales of themagnetic
fields in galaxy clusters.